For the sake of
an enhancement of
clarity we will now change the notation and abbreviate
\({\cal C}=Z_1\) 
(emphasizing the
geometry-determining role of the charge in \({\cal R}_1\) ) and
\({\cal P}=Z_2\) 
(underlining the analogous
auxiliary-metric-operator role of
the – possibly, generalized – parity
in \({\cal H}_{math}={\cal R}_2\) ).
Another
abbreviation
will be used to emphasize the privileged status
of the specific physical metric
\(\Theta _{(Bender)}={\cal PC}=Z_2Z_1=Y_2\,\)  of Eq. (REF ).
Marginally, we might add that
in the literature
the reference to the “parity” survived
even when the operator
\({\cal P}=Z_2\,\)  itself
(re-denoted by Greek lower-case \(\eta \)  in [1]}
and required to be self-adjoint in \({\cal R}_2\) ,
\(Z_2=Z_2^\dagger \) )
ceased to be immediately connected
with spatial reflection (check also [2]}).
